I have had good luck growing crown chips and other rootless pieces in potting soil placed in fabric grow bags. The grow bags don't hold on to moisture so instead of overwatering, you just have to start and maintain a 4-day watering cycle (maybe 3 days when it really gets hot). In the summer months, I move my bagged peonies onto the porch where they enjoy some shade.
If you do this, you might try to keep the tips of the stems at or very near the surface. Use a 3 gallon grow bag if you have or can get one.
And for what it's worth, that piece in the first photos looks particularly viable. But you're going to spend at least an extra year getting it nursed into something that can survive out in the soil.
I have a number of 2-year or 3-year projects
One of them was a piece of crown that looked about like a silver-dollar and it actually seems to be doing well. I've also planted quite a few eyeless roots just to test growing adventitious roots. Anyhow, the point of mentioning it is that things do end-up working out, it is just a matter of time and effort.
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